Graph Colorings: Topological Lower Bounds

In his remarkable proof from 1978 of the Kneser conjecture, László Lovász, for the first time, used tools from Algebraic Topology to obtain lower bounds on the chromatic number of a graph. For this, he associated certain simplicial (respectively cell) complexes to a graph and then exploited topological invariants of the resulting spaces.

In this project we focus on the geometric, topological, and combinatorial properties of certain interesting classes of coloring complexes.